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Previous articleNext article FreeCommentMarc P. GiannoniMarc P. GiannoniFederal Reserve Bank of Dallas Search for more articles by this author Federal Reserve Bank of DallasPDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreI. IntroductionSince Phillips (1958), economists have sought to estimate a Phillips curve relationship or a positive relation between inflation, πt, and a measure of the output gap, xt. Although historically such a relationship could be easily detected, the Phillips curve appears to have flattened in the United States more recently. Some authors have suggested that inflation does not depend on slack, that it is largely exogenous. This raises the key question: What changed? The answer to that question is critical for much of macroeconomics and in particular for monetary policy. With most central banks around the world seeking to stabilize inflation around a target level (e.g., 2% in the United States), it is crucial to understand the determinants of inflation and to know whether monetary policy can still affect inflation.Several potential explanations have been provided for the flattening of the Phillips curve. Some have suggested that structural changes in the economy in recent decades have played a significant role (e.g., Duca 2019). In many of models of sticky prices, more rigid prices than in the past or increases in market concentration and pricing power (De Loecker and Eeckhout 2017) could also result in a flattening of the Phillips curve. McLeay and Tenreyro argue instead that monetary policy itself is responsible for the flattening of the Phillips curve. The explanation is simple: If the central bank conducts optimal monetary policy, seeking to minimize deviations of inflation from target and output from potential output, then it should set its policy instruments to increase inflation when output is below potential and vice versa. It follows that optimal policy causes a negative correlation between inflation and the output gap. That negative correlation blurs in turn the positive correlation implied by the Phillips curve, so that in equilibrium, the correlation between inflation and the output gap may be positive, negative, or null, depending on the variability of shocks perturbing either the Phillips curve or the optimal policy relationship. The authors make the point very clearly through a sharp and elegant analysis, in the context of a simple New Keynesian model.After exposing the identification problem in estimating the slope of a Phillips curve, McLeay and Tenreyro propose strategies to estimate the Phillips curve and present evidence of a robust Phillips curve in the United States. This is a very nice and transparent paper that should be read by all of those who are interested in understanding and estimating the Phillips curve.In the remainder of this discussion, I will briefly review the authors’ story in the historical context and will quibble in Section III with the authors’ proposed identification of the Phillips curve, focusing in particular on the role of expectations.II. The StoryA key point of the paper is that one should distinguish between (i) a reduced-form Phillips curve, that is, an empirical relationship between inflation and a measure of the output gap, and (ii) a structural Phillips curve, that is, the underlying relationship between inflation, the output gap, inflation expectations, and possibly other factors, resulting from the firms’ optimal setting of their prices. In the debate about the flattening of the Phillips curve, the two concepts are often mixed, as the structural Phillips curve may be difficult to identify. As the authors make clear, optimal policy can lead to a flattening or even a negative relationship between inflation and the output gap in the reduced-form Phillips curve, even though there is a well-defined positively sloped underlying structural Phillips curve. The authors’ result does not rely on assuming that the policy maker conducts optimal policy under discretion and that it has a quadratic objective function. Consider the standard (structural) New Keynesian Phillips curve (eq. [1] in the paper) that characterizes the trade-off between inflation, πt, and the output gap, xt, faced by the central bank:(1)πt=βEtπt+1+κxt+ut,with a slope κ that is positive by assumption. In the face of “cost-push shocks,” ut, it is generally not possible to stabilize both inflation and the output gap. Suppose that the central bank can control the output gap, for example, via a short-term policy rate; that it observes ut and that it seeks to stabilize inflation at its target (πt=0) as in the case of a pure inflation-targeting regime. Optimal policy would then imply that the output gap respond negatively to the cost-push shockxt=−κ−1utso that, in equilibrium, inflation and hence inflation expectations are completely stabilized around the inflation target:πt=0,Etπt+1=0,as illustrated by the x-axis in figure 1 (which is adapted from figure 3 in the paper). The implication of this policy is that inflation would be uncorrelated swith the output gap. In other words, even though the underlying structural Phillips curve implies a positive relationship between inflation and the output gap, inflation targeting gives rise to a flat reduced-form Phillips curve relationship, with inflation apparently unrelated to the output gap.Fig. 1. Structural Phillips curve and optimal policyView Large ImageDownload PowerPointIn the case that the central bank cares both about inflation and output gap deviations from target, as the authors point out, optimal policy under discretion gives rise to a negative relationship between inflation and the output gap. Indeed, when the central bank seeks to minimize the loss function:(2)E0∑t=0∞βt[πt2+λxt2],subject to the behavior of the private sector represented by the structural Phillips curve (eq. [1]), optimal policy under discretion, that is, taking private sector expectations Etπt+j, Etxt+j as given, results in the optimal targeting rule:(3)πt=−λκxt,which states that the central bank seeks to increase inflation when output is below potential and vice versa, as illustrated by the downward-sloping gray line in figure 1. As exogenous shocks ut shift the Phillips curve but not the optimal policy relation (eq. [2]), equilibrium realizations of inflation and the output gap draw not the Phillips curve but rather the optimal target criterion (eq. [2]). In equilibrium, πt, xt depend only on utπt=λκ2+λ(1−βρ)ut,xt=−κκ2+λ(1−βρ)ut,where ρ is the degree of serial correlation in ut so that the covariance between inflation and the output gapcov(πt,xt)=−λκ(κ2+λ(1−βρ))2var(ut)<0is necessarily, and the correlation corr(πt,xt)=−1.A. Targeting Rule versus Taylor RuleSome readers may find a target criterion of the form (eq. [3]) to be unrealistic. We should however note that its characterization of monetary policy is not too different from that under a conventional Taylor rule. Indeed, the optimal target criterion (eq. [3]) implies that the policy rate it is set so as to satisfy πt+(λ/κ)xt=0. The policy rate can thus be related to inflation and the output gap according to a conventional Taylor-type rule:it=ϕ(πt+λκxt)with a large coefficient ϕ(→∞). If, in addition, policy makers care to also stabilize other variables such as the interest rate, then the optimal policy response to inflation and the output gap would likely be of a similar form but with a smaller coefficient 0<ϕ<∞, and the optimal interest rate would in addition respond to these other variables (e.g., the lagged interest rate).B. Historical ContextAs the authors recognize, the flattening or disappearance of an empirical relationship such as the reduced-form Phillips curve as a consequence of a successful monetary policy is an old idea that goes back at least to Kareken and Solow (1963), who emphasized that if monetary policy succeeds at offsetting all shocks that affect income, then we would observe fluctuations in money growth and a perfectly steady path for income. Similar ideas have been reinforced and generalized by many authors since then, most prominently with Goodhart’s “law” (1981)1 and the Lucas (1976) critique,2 and it is still mentioned in recent work (e.g., Hooper, Mishkin, and Sufi 2019). Unfortunately, it appears that much of the profession is quick to forget these powerful lessons when the empirical relationship between two key macroeconomic variables appears to have weakened, and so it is important that McLeay and Tenreyro remind us of this. As we learned from Lucas (1976), these lessons do not apply merely to relationships between two macroeconomic variables; they can be more pervasive. For instance, when Boivin and Giannoni (2006) documented the fact that impulse response functions of inflation and output to an unexpected 25 basis points change in the federal funds rate had become more muted in the post-1980 period, compared with the 1960–80 period, they asked whether this was due to a structural change in the economy (such as a flattening of the structural Phillips curve or a diminished sensitivity of economic activity to interest rate changes) or to a change in policy itself; they found that a more aggressive stance of policy toward inflation stabilization in the post-1980 period could explain most if not all of the change in estimated impulse response functions.III. Identifying the Structural Phillips CurveAside from making it very clear that one should not conclude that the Phillips curve has disappeared based on correlations between inflation and the output gap, or simple regressions, McLeay and Tenreyro describe in simple terms the identification problem, propose ways to address it, and provide evidence that there is a structural Phillips curve with positive slope between inflation and the output gap. As figure 1 illustrates, cost-push shocks ut help trace the policy rule, not the Phillips curve. If the policy rule is itself subject to disturbances et so that it becomes(4)πt=−λκxt−et,then fluctuations in et may help trace the structural Phillips curve. The identification problem arises when we face shocks to both the policy (targeting) rule and the Phillips curve.Focusing on equations (1) and (4) provides a transparent way of characterizing the identification problem, in a near-static environment (for given inflation expectations), in which the Phillips curve implies a positive contemporaneous relation between πt and xt, whereas policy implies a negative contemporaneous relation between these two variables. If only we could control for the cost-push shocks ut, then shocks to the policy rule (represented by the downward-sloping gray line in fig. 1) would trace out the structural Phillips curve. Similarly, the identification problem can be partly addressed in the case of regional Phillips curve subject to region-specific cost-push shocks, but with monetary policy responding to aggregate economic conditions, as McLeay and Tenreyro as well as other recent studies have proposed (Hooper et al. 2019).A. Difficulties with Identification via Disturbances to the Optimal Target CriterionAlthough the authors make a strong case for identifying the Phillips curve using equations (1) and (4), I am concerned that it may not be as easy to identify the Phillips curve in more complicated setups, in particular when the policy rule disturbances et are not exogenous and depend on other variables, including variables affecting the residuals ut themselves, or if the residuals ut capture more than exogenous cost-push shocks, indeed if they depend on variables that also shift the policy rule.To illustrate this point, I consider a few examples:• Take again the simple Phillips curve (eq. [1]) and the objective function (eq. [2]), but assume that optimal policy is conducted under commitment. Then, as pointed out by McLeay and Tenreyro, optimal policy can be represented by an optimal target criterion of the form (eq. [4]) with et=−(λ/κ)xt−1. If the cost-push shock is serially correlated, then et and ut are correlated. A suitable instrument is thus needed.• Assume instead that inflation involves some inertia as modeled, for example, in Christiano, Eichenbaum, and Evans (2005), and as appears realistic in the data. Then, as shown in Giannoni and Woodford (2004, eq. [12]), lagged inflation appears both in the Phillips curve (eq. [1]) and in the optimal target criterion (eq. [4]), so that et and ut would both be functions of lagged inflation.• When the representative household faces habit persistence in expenditures, then again, as shown in Giannoni and Woodford (2004, eq. [47] and eq. [53]), both the Phillips curve and the optimal target criterion involve the lagged output gap, so that ut and et in equations (1) and (4) would be both functions of xt−1 and hence would be correlated.• Suppose, alternatively, that the policy maker faces a Phillips curve of the form (eq. [1]) but cares about interest rate variability in addition to the two other terms entering the objective function (eq. [2]). Then, the optimal target criterion involves a relationship between current and forecasts of inflation, output gaps, as well as lags of the output gap and interest rates (see Giannoni and Woodford 2004; eq. [22]). Again, that would imply that the terms ut and et in equations (1) and (4) would be correlated.Similar concerns arise when the model involves both price and wage stickiness, so that a Phillips curve arises for price and for wage inflation; when monetary policy actions have delayed effects on macroeconomic variables, so that optimal policy depends on expectations of future inflation and output gaps; and so on.B. Identifying the Phillips Curve: Static versus DynamicAlthough McLeay and Tenreyro make an important conceptual point and provide a very intuitive way of characterizing the difficulty in identifying the Phillips curve in a near-static framework, I am skeptical that one can fully recover the Phillips curve without taking a stronger stance on dynamic relationships linking the key macroeconomic variables. The simple New Keynesian Phillips curve considered is an invaluable tool to develop intuition, but much of the empirical literature suggests that inflation responds to measures of slack in a more inertial fashion. Similarly, whereas the simple model considered assumes that policy makers can instantaneously affect economic activity and the output gap, empirical evidence suggests the effects are more sluggish. (If not, it would be difficult to explain why inflation has been below its target and economic activity has been below estimates of its potential for so many years following the Great Recession.) This implies that the dynamic relationship between inflation and the output gap is more complex than described by the simple New Keynesian model and that it is important to properly model these dynamics to identify a Phillips curve.Estimated dynamic stochastic general equilibrium (DSGE) models are a valuable tool to characterize the joint dynamics of key macroeconomic variables and thus of the complex interactions between the Phillips curve and policy. In such dynamic models, inflation expectations play a key role, and a monetary policy aimed at stabilizing inflation and hence inflation expectations does also imply a flattening of the reduced-form Phillips curve. A potential downside of such fully specified models is that they are necessarily misspecified. A key question, then, is whether such models can explain important recent episodes. In particular, Del Negro, Giannoni, and Schorfheide (2015) study whether a standard DSGE model along the lines of Christiano et al. (2005) and Smets and Wouters (2007) augmented with financial frictions and estimated with data up to 2008Q3 can explain the US macroeconomic behavior during and after the Great Recession. They find that as soon as credit spreads jump in the fall of 2008, the model successfully predicts the sharp contraction in activity and the modest and protracted decline in inflation, as shown in figure 2. They also find that data on credit spreads and inflation expectations, in addition to the standard data series used by, for example, Smets and Wouters (2007), are important in properly characterizing the state of the economy.Fig. 2. Dynamic stochastic general equilibrium (DSGE) model forecast of gross domestic product (GDP) growth, the output gap, and GDP deflator inflation, based on the model in Del Negro et al. (2015). Out-of-sample forecast starting in 2008Q4 (dotted lines); data used in estimation (solid lines); and ex post realization of the data (dashed lines).View Large ImageDownload PowerPointTo understand why inflation does not collapse given the sharp drop in output, it is useful to consider a simplified version of the forward-looking Phillips curve considered in the model. That simplified Phillips curve, which is similar to equation (1)—except that xt is replaced with real marginal costs—implies that inflation does not depend only on the current gap (or marginal cost), but on the entire path of future gaps:πt=∑j=0∞βjEt[κxt+j︸gaps+ut+j︸mark-up shocks].It follows that inflation and inflation expectations in the model remain well anchored, despite the sharp collapse in output, because monetary policy is expected to be aggressive enough to close the gaps in the future.Similarly to McLeay and Tenreyro, although the model includes a structural Phillips curve that involves a positive relationship between inflation and the output gap, inflation was predicted to move relatively little in the face of the output collapse. However, in contrast to McLeay and Tenreyro, according to the DSGE model, it was not the contemporaneous monetary stimulus (at the end of 2008 and in early 2009) that helped stabilize inflation; indeed, short-term nominal rates were constrained by the zero lower bound at that time. Instead, the expectation of future stimulus induced expectations of closing output gaps in the future and hence helped keep inflation near its target.IV. ConclusionMcLeay and Tenreyro have written a very nice paper that clearly and elegantly exposes the identification problem in estimating the slope of a Phillips curve when policy makers seek to stabilize inflation and/or the output gap. They propose interesting strategies to estimate the Phillips curve and present evidence of a robust Phillips curve in the United States. The simplicity of the framework considered allows the authors to provide numerous insights. I have expressed some reservations about the ability to generalize the results beyond the current framework, in particular when one faces more complex dynamic interactions between inflation, inflation expectations, activity, and policy. In more complicated environments, I suspect that DSGE model estimation remains necessary to better characterize the joint dynamics of macro variables, and the role of expectations.Endnotes. Author email address: Giannoni ([email protected]). The views expressed in this discussion are those of the author and do not necessarily represent those of the Federal Reserve Bank of Dallas or the Federal Reserve System. For acknowledgments, sources of research support, and disclosure of the author’s material financial relationships, if any, please see https://www.nber.org/chapters/c14246.ack.1. Goodhart (1981, 116): “Any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes.”2. 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